INEVITABLY, the first question on the lips of the film industry following the death Sunday of Stanley Kubrick was: What will happen to his final film, “Eyes Wide Shut”? Especially since, while early buzz on the film is good, there have been rumors that the erotic thriller, starring Tom Cruise and Nicole Kidman, is so sexually explicit that it could be saddled with an NC-17 rating.

(Previous NC-17 movies have included “Henry and June” and “Crash.” Traditionally, filmmakers have been opposed to the rating, arguing that it censors creative freedom by limiting the audience, bookings and advertising opportunities. As one filmmaker cynically put it: If you show a nipple being caressed, you get an NC-17; if you show a nipple being sliced off with a razor blade, you just get an R.)

Nonetheless, the NC-17 rating could damage the film’s moneymaking potential, because many suburban mall theaters will not book NC-17 movies, and some newspapers will not publish ads for them.

But even if “Eyes Wide Shut” does garner an NC-17 – and Warner Bros. will lobby mightily for an R rating – Kubrick’s work is untouchable. His deal with the studio gave him the right of “final cut,” and Hollywood insiders say that despite the risks inherent in an NC-17 rating, there is no chance that the studio would attempt to make any changes in the movie, whatever the legal technicalities may be.

For one thing, Kubrick long enjoyed a unique freedom in his relationship with the studios; his relationship with Warner Bros. predates the present regime of Terry Semel and Bob Daley. Warners was loyal to him, and vice versa.

As one executive told The Post, on condition of anonymity, “Even if it was terrible – and I doubt it is – no one would dare f— with his cut – not now, not a chance. That’s an absurd notion.”

Other experts point out that Kubrick’s movies always attracted vast worldwide media interest; any hint that the studio messed around with the great man’s last work would provoke a savage response and probably damage the film’s commercial prospects.

And if any more insurance were needed, the clout of Tom Cruise – who stars in the film with his wife, Nicole Kidman, and who was devoted to Kubrick – makes it certain that the film will be released in Kubrick’s cut.